#### Answer

$$10m^2(6m-n)(m-5n)$$

#### Work Step by Step

Factor out the greatest common factor from all the terms in the expression, in this case, $10m^2$,
$$60m^4-120m^3n+50m^2n^2=10m^2(6m^2-12mn+5n^2)$$
Next factor the trinomial. The possible factors of $6m^2$ are $6m$ and $m$ or $3m$ and $2m$. The possible factors of $5n^2$ are $5n$ and $n$. Test different combinations to find the set that works.
$$=10m^2(6m-n)(m-5n)$$